London is one of those strange cities where the population is so large that it's like a country on it's own. Yes it's true that there are slums, particularly on the outskirts where they will beat you up and stab you for a stick of gum, but if you just stick to the central tourist locations during the day you really have very little to worry about. Of course there are pick pockets around, but no more so than any other big city.

Maybe replacing that flashy D800 strap with a more discrete one would be a good idea though.